# interest rates

## The Difference Between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) Explained

by on October 31, 2011

in Finance

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Quite a number of readers had written in asking me to explain the difference between APR and APY.

APR = Annual Percentage Rate. Think of this as simple interest.

APY = Annual Percentage Yield. Think of this as compound interest.

APR and APY explain why your Fixed Deposit certificate quotes an interest rate of 9% but upon maturity you get an interest amount that is slightly higher than what you’d actually get at 9%.

APY = APR compounded at a certain compounding interval.

The exact formula that relates these two is:

APY = (((1 + (Quoted_APR/100)/Compounding_Interval)^Compounding_Interval) – 1)*100

Look at this illustration (click on the image for a full-size version). When APR = 10.25% and compounding is done quarterly then,

APY = (((1 + (10.25/100)/4)^4) – 1)*100 = 10.65%

On the other hand, if APR = 10.50% and compounding is done quarterly then,

APY = (((1 + (10.50/100)/4)^4) – 1)*100 = 10.92%

Finally, if APR = 10.25% and compounding is done semi-annually then,

APY = (((1 + (10.25/100)/2)^2) – 1)*100 = 10.51%

That explains the difference between APR and APY. Let me know if you have any questions.

Note: With Credit Cards you might sometimes see a monthly-APR quoted such as 3.1% per month. Simply multiply this by 12 to get the annual-APR. In this case, the annual-APR is 3.1% x 12 = 37.2%.